////////////////////////////////////////////////////////////////////// 
// libsrc/Random.cpp 
// (c) 2000-2008 Goncalo Abecasis
// 
// This file is distributed as part of the MaCH source code package   
// and may not be redistributed in any form, without prior written    
// permission from the author. Permission is granted for you to       
// modify this file for your own personal use, but modified versions  
// must retain this copyright notice and must not be distributed.     
// 
// Permission is granted for you to use this file to compile MaCH.    
// 
// All computer programs have bugs. Use this file at your own risk.   
// 
// Saturday April 12, 2008
// 
 

//////////////////////////////////////////////////////////////////////////////
// This file includes code derived from the original Mersenne Twister Code
// by Makoto Matsumoto and Takuji Nishimura
// and is subject to their original copyright notice copied below:
//////////////////////////////////////////////////////////////////////////////

//////////////////////////////////////////////////////////////////////////////
// COPYRIGHT NOTICE FOR MERSENNE TWISTER CODE
// Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions
// are met:
//
// 1. Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// 2. Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// 3. The names of its contributors may not be used to endorse or promote
// products derived from this software without specific prior written
// permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
///////////////////////////////////////////////////////////////////////////////

#include "Random.h"
#include "MathConstant.h"
#include "Error.h"

#include <math.h>

//Constants used internally by Mersenne random number generator
#define MERSENNE_N 624
#define MERSENNE_M 397

// constant vector a
#define MATRIX_A 0x9908b0dfUL

// most significant w-r bits
#define UPPER_MASK 0x80000000UL

// least significant r bits
#define LOWER_MASK 0x7fffffffUL


// Constants used internally by Park-Miller random generator
#define IA 16807
#define IM 2147483647
#define AM (1.0 / IM)
#define IQ 127773
#define IR 2836
#define NTAB 32
#define NDIV (1+(IM-1)/NTAB)
#define RNMX (1.0-EPS)

Random::Random(long s)
   {
#ifndef __NO_MERSENNE
   mt = new unsigned long [MERSENNE_N];
   mti = MERSENNE_N + 1;
   mersenneMult = 1.0/4294967296.0;
#else
   shuffler = new long [NTAB];
#endif
   Reset(s);
   }

Random::~Random()
   {
#ifndef __NO_MERSENNE
   delete [] mt;
#else
   delete [] shuffler;
#endif
   }

void Random::Reset(long s)
   {
   normSaved = 0;

#ifndef __NO_MERSENNE
   InitMersenne(s);
#else
   // 'Continuous' Random Generator
   if ((seed = s) < 1)
      seed = s == 0 ? 1 : -s;  // seed == 0 would be disastrous

   for (int j=NTAB+7; j>=0; j--)  // Warm up and set shuffle table
      {
      long k = seed / IQ;
      seed = IA * (seed - k * IQ) - IR * k;
      if (seed < 0) seed += IM;
      if (j < NTAB) shuffler[j] = seed;
      }
   last=shuffler[0];
#endif
   }

// initializes mt[MERSENNE_N] with a seed
void Random::InitMersenne(unsigned long s)
   {
   mt[0]= s & 0xffffffffUL;
   for (mti = 1; mti < MERSENNE_N; mti++)
      {
      mt[mti] = (1812433253UL * (mt[mti-1] ^ (mt[mti-1] >> 30)) + mti);
      /* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */
      /* In the previous versions, MSBs of the seed affect */
      /* only MSBs of the array mt[].  */
      /* 2002/01/09 modified by Makoto Matsumoto */

      mt[mti] &= 0xffffffffUL;
      }
   }

int Random::Binary()
   {
   return Next() > 0.5 ? 1 : 0;
   }

#ifndef __NO_MERSENNE

double Random::Next()
   {
   unsigned long y;

   // mag01[x] = x * MATRIX_A for x=0,1
   static unsigned long mag01[2]={0x0UL, MATRIX_A};

   if (mti >= MERSENNE_N)
      {
      /* generate MERSENNE_N words at one time */
      int kk;

      // If InitMersenne() has not been called, a default initial seed is used
      if (mti == MERSENNE_N+1)
         InitMersenne(5489UL);

      for (kk=0; kk < MERSENNE_N-MERSENNE_M; kk++)
         {
         y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
         mt[kk] = mt[kk+MERSENNE_M] ^ (y >> 1) ^ mag01[y & 0x1UL];
         }

      for (; kk < MERSENNE_N-1; kk++)
         {
         y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
         mt[kk] = mt[kk+(MERSENNE_M - MERSENNE_N)] ^ (y >> 1) ^ mag01[y & 0x1UL];
         }

      y = (mt[MERSENNE_N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
      mt[MERSENNE_N-1] = mt[MERSENNE_M-1] ^ (y >> 1) ^ mag01[y & 0x1UL];

      mti = 0;
      }

   y = mt[mti++];

   // Tempering
   y ^= (y >> 11);
   y ^= (y << 7) & 0x9d2c5680UL;
   y ^= (y << 15) & 0xefc60000UL;
   y ^= (y >> 18);

   return (mersenneMult * ((double) y + 0.5));
   }

// Generates a random number on [0,0xffffffff]-interval

unsigned long Random::NextInt()
   {
   unsigned long y;

   // mag01[x] = x * MATRIX_A for x=0,1
   static unsigned long mag01[2]={0x0UL, MATRIX_A};

   if (mti >= MERSENNE_N)
      {
      /* generate MERSENNE_N words at one time */
      int kk;

      // If InitMersenne() has not been called, a default initial seed is used
      if (mti == MERSENNE_N + 1)
         InitMersenne(5489UL);

      for (kk= 0; kk < MERSENNE_N - MERSENNE_M; kk++)
         {
         y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
         mt[kk] = mt[kk+MERSENNE_M] ^ (y >> 1) ^ mag01[y & 0x1UL];
         }

      for (; kk< MERSENNE_N-1; kk++)
         {
         y = (mt[kk] & UPPER_MASK) | (mt[kk+1] & LOWER_MASK);
         mt[kk] = mt[kk+(MERSENNE_M - MERSENNE_N)] ^ (y >> 1) ^ mag01[y & 0x1UL];
         }

      y = (mt[MERSENNE_N-1] & UPPER_MASK) | (mt[0] & LOWER_MASK);
      mt[MERSENNE_N-1] = mt[MERSENNE_M-1] ^ (y >> 1) ^ mag01[y & 0x1UL];

      mti = 0;
      }

   y = mt[mti++];

   // Tempering
   y ^= (y >> 11);
   y ^= (y << 7) & 0x9d2c5680UL;
   y ^= (y << 15) & 0xefc60000UL;
   y ^= (y >> 18);

   return y;
   }

#else

double Random::Next()
   {
   // Compute seed = (IA * seed) % IM without overflows
   // by Schrage's method
   long k = seed / IQ;
   seed = IA * (seed - k * IQ) - IR * k;
   if (seed < 0) seed += IM;

   // Map to 0..NTAB-1
   int j = last/NDIV;

   // Output value is shuffler[j], which is in turn replaced by seed
   last = shuffler[j];
   shuffler[j] = seed;

   // Map to 0.0 .. 1.0 excluding endpoints
   double temp = AM * last;
   if (temp > RNMX) return RNMX;
   return temp;
   }

unsigned long Random::NextInt()
   {
   // Compute seed = (IA * seed) % IM without overflows
   // by Schrage's method
   long k = seed / IQ;
   seed = IA * (seed - k * IQ) - IR * k;
   if (seed < 0) seed += IM;

   // Map to 0..NTAB-1
   int j = last/NDIV;

   // Output value is shuffler[j], which is in turn replaced by seed
   last = shuffler[j];
   shuffler[j] = seed;

   return last;
   }

#endif

double Random::Normal()
   {
   double v1, v2, fac, rsq;

   if (!normSaved)  // Do we need new numbers?
      {
      do {
      v1 = 2.0 * Next() - 1.0;  // Pick two coordinates from
      v2 = 2.0 * Next() - 1.0;  // -1 to +1 and check if they
      rsq = v1*v1 + v2*v2;  // are in unit circle...
      } while (rsq >= 1.0 || rsq == 0.0);

      fac = sqrt(-2.0 * log(rsq)/rsq);  // Apply the Box-Muller
      normStore = v1 * fac;  // transformation and save
      normSaved = 1;  // one deviate for next time
      return v2 * fac;
      }
   else
      {
      normSaved = 0;
      return normStore;
      }
   }

void Random::Choose(int * array, int n, int k)
   {
   int choices = 1, others = 0;

   if (k > n / 2)
      {
      choices = 0;
      others = 1;
      k = n - k;
      }

   for (int i = 0; i < n; i++)
      array[i] = others;

   while (k > 0)
      {
      int i = NextInt() % n;

      if (array[i] == choices) continue;

      array[i] = choices;
      k--;
      }
   }

void Random::Choose(int * array, float * weights, int n, int k)
   {
   int choices = 1, others = 0;

   if (k > n / 2)
      {
      choices = 0;
      others = 1;
      k = n - k;
      }

   // First calculate cumulative sums of weights ...
   float * cumulative = new float [n + 1];

   cumulative[0] = 0;
   for (int i = 1; i <= n; i++)
      cumulative[i] = cumulative[i - 1] + weights[i - 1];

   float & sum = cumulative[n], reject = 0.0;

   for (int i = 0; i < n; i++)
      array[i] = others;

   while (k > 0)
      {
      float weight = (float) Next() * sum;

      int hi = n, lo = 0, i = 0;

      while (hi >= lo)
         {
         i = (hi + lo) / 2;

         if (cumulative[i + 1] <= weight)
            lo = i + 1;
         else if (cumulative[i] >= weight)
            hi = i - 1;
         else break;
         }

      if (array[i] == choices) continue;

      array[i] = choices;
      reject += weights[i];

      // After selecting a substantial number of elements, update the cumulative
      // distribution -- to ensure that at least half of our samples produce a hit
      if (reject > sum * 0.50)
         {
         cumulative[0] = 0;
         for (int i = 1; i <= n; i++)
            if (array[i] != choices)
               cumulative[i] = cumulative[i - 1] + weights[i - 1];
            else
               cumulative[i] = cumulative[i - 1];

         reject = 0.0;
         }

      k--;
      }

   delete [] cumulative;
   }

Random globalRandom;


 
